Why is U$C-Notre Dame in there? To me a real rivalry should at least be between teams geographically close, or at least in the same conference. I don't think these teams even play each other in any sport besides football.
Now now now, let's not take a shot at one of my favorite $chool$. I seriously doubt if either the costs for attending, nor the average wealth of their alumni, would differ significantly between the two schools.
I will take a stab at answering your question though. One reason, IMHO, that it is such a big rivalry, is it was one of the first long distance rivalries ever developed. One which went a long way towards 'nationalizing' NCAA football. You have to recall that in 1926, the time, trouble and effort to make a journey of 1500 miles was significant. Add the fact that every other year, the ND fans could bask in California sunshine for several days before returning to the fall cold of South Bend, made this game one to really look forward to.
As a side comment, I will say that as much as I cannot stand ND, having attended 8 ND-USC games over the years, their fans are amongst the best and most sporting fans of any team that has ever visited the LA Coliseum.